You're right, LS: this is an old one! But being the DNA dweeb that I am, I took a quick look at the Randolph DNA Project data at FTDNA and, unfortunately, it has...some issues. Not counting the "Ungrouped" classification, it has 19 identified groups populated with, of course, only what I can see publicly.
A cursory check, though, shows that should be more on the order of 30 separate groupings, and some of the existing 19 should be combined (though I believe the admin is trying to do some separation by geography rather than genetics, which is a risky thing to do from an accuracy standpoint).
For example, "Group 3: Yancey County" and "Group 3A: FitzRandolphs" should not be grouped separately if the groupings are intended to be genetic. All nine kits shown in Group 3 are genetically related within FTDNA matching parameters to Group 3A. There are also five ungrouped or unassigned kits that belong in Group 3A, as well. Those kit numbers are 65475, 133687, 362014, 923087, and MK32490.
The SNP FGC44019 doesn't appear on the project's results (it's in the basal haplogroup J, not R), and FGC41938 is a child branch of FGC41936, which both roll up to U152, P312, and eventually to M269. So there is no discrepancy between those deep subclades and a tested or assumed M269.
If William Randolph of Turkey Island is the one from Henrico County that you referenced, then all five of the kits referenced in the results as "2C" are genetically grouped: these are the groups subtitled "Chesterfield Randolphs," "Turkey Island Virginia," and "United Kingdom"; they share a common male ancestor.
Beyond that quick look, I don't know anything about the Randolph clan, so will quietly walk away.